Quantitative Methods in Supply Chain Management: Models and Algorithms

410 Pages·2012·4.11 MB·English

by  Ioannis T. Christou (auth.)

Quantitative Methods in Supply Chain
Management

Ioannis T. Christou
Quantitative Methods in
Supply Chain Management
Models and Algorithms
123
Prof.Ioannis T.Christou
Athens InformationTechnology
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ISBN 978-0-85729-765-5 e-ISBN978-0-85729-766-2
DOI 10.1007/978-0-85729-766-2
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Preface
This book presents some of the most important methods and tools available for
modeling and solving problems arising in the context of supply chain manage-
ment; in the context of this book, ‘‘solving problems’’ usually means ‘‘designing
efficient algorithms for obtaining high-quality solutions’’. Modeling a real-world
problemsothatitbecomesamenabletoanalysisandthelaterdesignofalgorithms
foractuallysolvingitisafascinatingmixtureofart,science,andengineering.The
major purposeof thisbook is therefore toshow what modeling techniques can be
expected to work for a given situation, as well as what kinds of constraints or
objective functions can render models intractable, and what to do when omitting
them is not an option; above all, how to apply existing proven exact or heuristic
methods, or even design a hybrid or completely new algorithm for a particular
model.
Asisoftenthecasewithtextbooks,thematerialinthisbookgrewoutofasetof
lecturesthatIgavetoM.Sc.studentsofCarnegie-MellonUniversity’sMaster’sin
Information Networking program, and Ph.D. level graduate students at Aalborg
University, Aalborg, Denmark on the topics of Business Management for Engi-
neers, Supply Chain Management and Logistics, and Network Optimization. The
enthusiasm of my students encouraged me to carefully write my lecture notes in
book form, and the end result is this book.
The content of the book is organized as follows: the first chapter is a review
chapteronmethodsforcontinuousaswellascombinatorialoptimization.Itcovers
most areas of modern optimization:
• Unconstrainednon-linearoptimization,wherethemainfocusisonmethodsthat
converge to a local optimum or at least a saddle point, including Newton-like
methods,conjugate-gradientmethods,andtrust-regionmethods,butthereisalso
a discussion on successful meta-heuristics for global optimization: simulated
annealing, evolutionary algorithms, genetic algorithms, the differential evolu-
tionmethod. Theoreticalresultsare giventoshow any guaranteethat amethod
has for convergence to a local optimum or a saddle point.
v
vi Preface
• Constrained linear optimization: the revised simplex method for linear pro-
gramming is covered in some detail, as is the revised network simplex method
for linear network optimization. Advanced topics in network optimization
including auction algorithms for the linear assignment problem are also
discussed.
• Constrained non-linear optimization: the first-order necessary conditions for
mathematical programming are given using the standard theorems of the
alternative, and first-order sufficient conditions are presented for convex func-
tions. From an algorithmic point of view, penalty methods and Lagrangean
multiplier methods are discussed.
• Combinatorial and mixed-integer optimization, where the focus is on the
frameworkoftheBranch-and-BoundmethodanditsvariantsincludingBranch-
and-Price, Branch-and-Cut-and-Price etc. Successful meta-heuristics including
Tabu search and the more recent nested partitions method are also covered.
The chapter also includes an introduction to dynamic programming, which
plays an important role on many problems inplanning, scheduling, and inventory
control. All the material in this chapter can be considered classical, with the
exception ofthe recent introduction ofthe nested partitionsmethod in the arsenal
of people working on NP-hard combinatorial optimization problems. As such, it
can be skipped by readers familiar with the general (finite-dimensional) optimi-
zation techniques and serve only as a reference when the need arises.
The second chapter is an introduction to (short and medium term) demand
forecasting using mostly time-series analysis methods. Demand forecasting is a
tactical problemthatishoweverofgreatimportancetosupplychainmanagement
as it forms the basis for setting sales targets, production plans, and consequently
and even more seriously, lead-times, personnel levels and so on. Besides the
classical exponential smoothing methods and their many variants,and time-series
regression methods, and decomposition methods, there is a detailed derivation of
fast order-recursive methods (i.e. the Levinson-Durbin method) for solving the
Yule-Walker equations arising in auto-regressive based forecasting which is not
the standard material in such manuscripts. This is also the case for prediction
marketsandtheirinformationaggregationcapabilities,presentedinthatchapteras
well.Thematerialonensembleforecastsontheotherhand,isbasedmostlyonthe
author’s own research, and some computational results and conclusions are pre-
sented for the first time.
The third chapter is an introduction to tactical and operational level planning
and scheduling problems, seen from the point of view of the interface between
Operations Research and Computer Science. In this case, the focus is on formu-
lating accurate models that are at the same time amenable to efficient algorithms
for solving them to optimality or at least to near-optimality. Hierarchical pro-
duction planning is introduced as a vehicle for reducing problem complexity,
which then allows one to formulate optimization models at each level of the
hierarchythatcanbesolvedexactlyorforwhichfastandefficientheuristicsexist,
even for large-scale problems. The algorithms for crew assignment scheduling
Preface vii
problemsprovidedhereweredevelopedinthecontextofmyresearchonadvanced
decision support systemsat Lucent Bell Labs, Transquest, and DeltaTechnology.
Finally, the modeling of problems related to available-to-promise and order
admission control and corresponding solution techniques are comprehensively
presented here for the first time.
The fourth chapter deals with inventory control, a purely operational problem.
Thefocusismostlyonsingle-echelonsystems,butabriefdiscussionofthemulti-
echelon (serial) case is also presented. Starting with the simple case of deter-
ministic and constant demand and the EOQ model, the text quickly turns to the
much more challenging stochastic demand case. The material in this section
requires a good understanding of probability theory and statistics. The modeling
and analysis of such systems was completed more than forty years ago, but
algorithms–exactorheuristic–fordeterminingoptimalpolicyparametersofsome
such systems have not appeared until very recently. For example, at the time of
this writing, I have not been able to find any exact or heuristic algorithm for the
(s,S,T) policy optimization under stationary demand and linear holding and
backorder costs in the literature. In this chapter, both exact and fast heuristic
algorithms for all major inventory control policies are discussed in detail, and
computational results are provided.
The fifth chapter deals with the most strategic-level decision problems to be
made in supply chain management, which are however intimately linked to
operational-level decisionproblems:location theory anddistributionmanagement
problems.Anumberofrelatedlocationproblemsincludingthep-medianproblem,
the uncapacitated and the capacitated facility location problem, as well as multi-
echelon multi-commodity location/allocation problems are presented, modeled,
andanalyzedinthischapter,andefficientexactandheuristicmethodsaregivenfor
theirsolution.Somemethodsareagainpresentedhereforthefirsttime(thecluster
ensemble-based methods for the p-median and uncapacitated facility location
problem in particular). Regarding distribution management, some of the most
important techniques for vehicle routing problems under the general case of
resource constraints and time windows are discussed. Both exact algorithms
relying on column generation as well as carefully crafted heuristics are presented
for this type of problem.
The last chapter (epilogue) presents a list of some problem areas that I deem
will be of greatimportance in supply chain management inthe near future. Some
oftheseproblemsshouldbetackledviarigorousmethodswhereasotherproblems
are purely information technology problems that should be attacked via rigorous
software development techniques for building secure and dependable computing
systems.
The intended audience of this book is advanced undergraduate and graduate
students and researchers working on the interfaces of operations research and
computer science; such persons are often affiliated with operations research,
electricalandcomputerengineering,computerscience,andindustrialandsystems
engineering departments or graduate business schools. The prerequisites for
understanding the material in this book are fairly standard: a two-semester
viii Preface
undergraduate-level course on calculus and linear algebra should be enough to
follow the mathematical developments in the manuscript. A first course on pro-
gramminganddatastructuresisalsonecessarytobeabletoimplementmostofthe
algorithms inthis book. The material inChap. 4 also requires a good background
(i.e. a one-semester undergraduate-level course) of probability; some results
however are developed using the notions of stochastic convexity and its applica-
tions. Assuming the students have also had some exposure to optimization
methods,thematerialinChaps. 2–5canbepresentedinonefullsemester course.
Otherwise,appropriatesectionsfromtheoptimizationreviewfirstchaptermustbe
presented in a two- or three-week time span, and then selected topics from
Chaps.2–5canbepresentedintheremainingtime,probablyskippingthematerial
on auto-regressive methods from Chap. 2, and the material on inventory control
under stochastic demand in Chap. 4.
Atthispoint,Iwouldliketothankallmystudentswhocarefullyreadhard-to-
read portions of unfinished manuscripts of this book and made very useful sug-
gestions.Iwouldliketoespeciallythankmycolleague,Dr.SofoklisEfremidisfor
proof-reading the first drafts of chapter one of this book and suggesting many
corrections and improvements, my student Mr. Yongming Luo for carefully
readingthesecondchapterofthebookandpreparingsomeofthefiguresinit,and
finally, Mr. Panagiotis Apostolopoulos for reading parts of the third chapter and
makingusefulsuggestions.Andofcourse,Iwouldliketothanktheeditorialteam
at Springer for excellent job editing, formatting, and typesetting the book.
Lastbutnottheleast,Iwouldliketodedicatethisbooktomydaughter,Anna,
and to guarantee to her that I will make up for all the time that she did not get to
play with me while I was preparing this book.
Athens, February 2011
Contents
1 A Review of Optimization Methods . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Continuous Optimization Methods. . . . . . . . . . . . . . . . . . . . . . 2
1.1.1 Unconstrained Optimization . . . . . . . . . . . . . . . . . . . . 2
1.1.2 Constrained Optimization. . . . . . . . . . . . . . . . . . . . . . 41
1.1.3 Dynamic Programming. . . . . . . . . . . . . . . . . . . . . . . . 88
1.2 Mixed Integer and Combinatorial Optimization Methods . . . . . . 93
1.2.1 Mixed Integer Programming Modeling. . . . . . . . . . . . . 97
1.2.2 Methods for Mixed Integer Programming. . . . . . . . . . . 103
1.3 Bibliography. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
1.4 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
2 Forecasting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
2.1 Smoothing Methods for Time-Series Analysis. . . . . . . . . . . . . . 142
2.1.1 Na Forecast Method. . . . . . . . . . . . . . . . . . . . . . . . . . 142
2.1.2 Cumulative Mean Method . . . . . . . . . . . . . . . . . . . . . 143
2.1.3 Moving Average Method . . . . . . . . . . . . . . . . . . . . . . 144
2.1.4 Moving Average with Trends Method . . . . . . . . . . . . . 146
2.1.5 Double Moving Average Method . . . . . . . . . . . . . . . . 146
2.1.6 Single Exponential Smoothing Method. . . . . . . . . . . . . 148
2.1.7 Multiple Exponential Smoothing Methods . . . . . . . . . . 153
2.1.8 Double Exponential Smoothing with Linear
Trends Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156
2.1.9 The Holt Method. . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
2.1.10 The Holt–Winters Method . . . . . . . . . . . . . . . . . . . . . 159
2.2 Time-Series Decomposition . . . . . . . . . . . . . . . . . . . . . . . . . . 162
2.2.1 Additive Model for Time-Series Decomposition . . . . . . 163
2.2.2 Multiplicative Model for Time-Series
Decomposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165
2.2.3 Case Study. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166
ix